Answer: Let the legs of the right triangle be a and b. We know that the radius of the inscribed circle is 4 cm, which means that the inradius is also 4 cm. The inradius is given by:
r = (a + b - c)/2
where c is the hypotenuse, so we can substitute the given values to get:
4 = (a + b - 35)/2
Multiplying both sides by 2, we get:
8 = a + b - 35
Adding 35 to both sides, we get:
a + b = 43
We also know that the area of the triangle is given by:
A = (ab)/2
where a and b are the legs of the triangle. We can use the Pythagorean theorem to relate the legs to the hypotenuse:
a^2 + b^2 = c^2
Substituting the given value for the hypotenuse, we get:
a^2 + b^2 = 35^2
Simplifying, we get:
a^2 + b^2 = 1225
Now we can use the equation for the sum of the legs to solve for one of the legs in terms of the other:
a + b = 43
b = 43 - a
Substituting this expression for b into the equation for the area, we get:
A = (a(43 - a))/2
Simplifying, we get:
A = (43a - a^2)/2
To find the maximum value of the area, we can take the derivative of A with respect to a and set it equal to 0:
dA/da = 43/2 - a = 0
Solving for a, we get:
a = 43/2
Substituting this value into the equation for the area, we get:
A = (43/2)(43/2 - 43/2)/2 = 0
This means that the area of the triangle is 0 when one of the legs has a length of 0, which is not possible. Therefore, the maximum area occurs when the legs have equal lengths, which means that the right triangle is an isosceles right triangle. In this case, we have:
a = b = (35/sqrt(2)) cm
Substituting these values into the equation for the area, we get:
A = (ab)/2 = ((35/sqrt(2))^2)/2 = 612.5 cm^2
Therefore, the area of the right triangle is 612.5 square centimeters.
Step-by-step explanation:
A _______ distribution summarizes the information from one variable ONLY,without considering ANY information from another variable.A- joint ("and").B- conditional.C- marginal.
A joint ("and") distribution summarizes the information from one variable only, without considering any information from another variable.
Joint distribution mostly is based on joint probability, which also means it can be simply defined as the probability of two events also known as variables which happen to be happening together. These two events are usually coined event A and event B, and hence can formally be written as: p (A and B).
It also can be defined as the two-way frequency table, that is, a table which displays the frequencies or “counts” for two categorical variables.
Similarly a joint probability distribution is simply the description of the probability that a given individual takes on two specific values for the variables.
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The graph of f(x)=x² was translated 4 units to the right and horizontally compressed by a factor of 5 to create the graph of function g. Write an equation in vertex form to represent function g.
The vertex form of the quadratic equation g is:
g(x) = 25*(x - 4)²
How to find the equation for function g?We start with the parent quadratic function:
f(x) = x²
We know that first we apply a translation of 4 units to the right, so we will get:
g(x) = f(x - 4)
And then we compress it horizontally by a factor of 5, then we can write:
g(x) =f( 5(x - 4))
Replacing the actual function we will get:
g(x) = ( 5*(x - 4))²
Distributing the exponent we will get:
g(x) = 5² *(x - 4)²
g(x) = 25*(x - 4)²
That is the quadratic equation in vertex form.
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what is 1 gallon in oz?
The value 1 gallon has 128 fluid ounces(oz)
"How many ounces in a gallon?" This is one of the most frequently asked questions regarding liquid measurements. One gallon equals 8 pints, 4 quarts, or 16 cups. There are 128 fluid ounces in a gallon, and this number depends on whether you use imperial or metric units of measure.
There are 128 US fluid ounces in a US gallon. If you're in the UK, you'll find a gallon at 160 UK fluid ounces. This is because the US fluid gallon is smaller than the British imperial gallon (3,785 liters compared to
,5
6 liters). When converting
Gallons to Fluid Ounces, remember that the US Fluid Ounce is larger than the British Imperial Ounce. A US fluid ounce is 29.5735 ml. For comparison, a UK (Imperial) fluid ounce is 28.
131 ml. So the US has a smaller gallon than the UK, but a slightly larger fluid ounce. It's enough to make your head explode. For these two conversions you need the following information:
1 gallon (US) = 128 ounces (US, Fluid)
1 gallon (UK) = 160 ounces (UK, Fluid)
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Liam is setting up folding chairs for a meeting. If he arranges the chairs in 8 rows of the same length, he has 7 chairs left over. If he arranges the chairs in 6 rows of that same length, he has 19 left over. How many chairs does Liam have?
Answer: i think the answer would be 75
Answer:
55 chairs.
Step-by-step explanation:
Note the way Liam arranges the chairs.
1) He arranges chairs in 8 rows of the same length, with 7 chairs left over.
8x + 7
2) He arranges chairs in 6 rows of the same length, with 19 chairs left over:
6x + 19
Set the two expressions equal to each other:
8x + 7 = 6x + 19
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Subtract 6x and 7 from both sides of the equation:
8x (-6x) + 7 (-7) = 6x (-6x) + 19 (-7)
8x - 6x = 19 - 7
2x = 12
Next, divide 2 from both sides of the equation:
(2x)/2 = (12)/2
x = 12/2
x = 6
Plug in 6 for x in both expressions. It should give the same answer:
8x + 7
8(6) + 7 = (8 * 6) + 7 = (48) + 7 = 55
6x + 19
6(6) + 19 = (6 * 6) + 19 = (36) + 19 = 55
~
Therefore, Liam has 55 chairs in all.
~
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Find the missing measures This is rhombus ABCD
AB =14mm
ACD=58
ABD=32
E is the midpoint
a. AD =
b. m/CBD =
c. m/ADC =
d. m/AEB =
e. m/DAC =
Answer:
a. AD = 28 mm
b. m/CBD = 90°
c. m/ADC = 90°
d. m/AEB = 45°
e. m/DAC = 135°
Please, Help me with this question
how much is 1000 mcg to mg
To convert mcg to mg, divide the mcg value by 1000. Therefore:
1000 mcg = 1000/1000 mg = 1 mg
So, 1000 mcg is equal to 1 mg.
The graphs of function f ang g represent the height of an object being launched into the air as a function of time. Which object was in the air longer?
Function g lingered for a while.
What does the physics projectile equation mean?h = v 0 y 2 2 g . This equation, which only depends on the vertical component of the initial velocity, specifies the maximum height of a projectile above its launch site.
What is the projectile's maximum height formula?The projectile formula's maximum height from the graph is H = u 2 sin 2 2 g.
An item named g was launched from a higher location when x=0... g(0)> f(0).
A higher point was reached by the object of g.
When the object was launched, f's slope was greater than g's slope.
The launch velocity of object f was greater.
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Can someone tell me the domain and range for this function?
The domain is all real values and the range is y <= 3
How to determine the domain and the rangeFrom the question, we have the following parameters that can be used in our computation:
The graph
The domian is the set of the input values
In this case, the graph has no restriction on its input
So, we have
Domain = all set of real values
For the range, we have
Maximum y value = 3
So, we have
Range: y <= 3
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complete both transformations below then enter the final coordinaties of the figure below A(-6,-3) b (-1,-4) c (-5,-1) 1. reflect across x-axis 2. <3,-2>
The coordinates of the figure are A''(-3, 1),B''(2,2), C''(-2, -1).
What is the transformation of a point?
The transformation, or f: X →X, is the name given to a function, f, that maps to itself. After the transformation, the pre-image X becomes the image X. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one direction or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point. Two-dimensional mathematical figures move about a coordinate plane according to transformations.
Given that the coordinates of the points A, B, C are A(-6,-3), B(-1,-4), C(-5,-1).
The rule of a reflection across the x-axis is (x,y)→(x,-y).
After reflection across the x-axis,
A(-6,-3)→ A'(-6,3)
B(-1,-4)→B'(-1,4)
C(-5,-1)→C'(-5,1)
A rule of translation of 3 units right and 2 units down is (x,y)→(x+3,y-2).
Thus the new coordinates are:
A'(-6,3)→ A''(-6+3,3-2)=A''(-3,1)
B'(-1,4)→ B''(-1+3,4-2)=B''(2,2)
C'(-5,1)→ C''(-5+3,1-2)=C''(-2,-1)
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Identify the vertex, axis of symmetry and whether the vertex is a minimum or maximum for the given function.
f(x)=2(x+1)^2-6
The vertex is (-1, -6) and the axis of symmetry is -1. The function is minimum. The solution has been obtained by using equation of parabola.
What is a parabola?
Any point on a parabola is equally separated from both the focus, or predetermined point, and the fixed straight line (known as the directrix).
We are given f(x) = 2(x + 1)² - 6
We know that a parabola of equation a(x - h)² + k always has its vertex at (h, k) with axis of symmetry at x = h.
So, the vertex here is (-1, -6) and the axis of symmetry is x = -1.
It is a minimum function because there is a positive value before (x - h)².
Hence, the vertex is (-1, -6) and the axis of symmetry is -1 and the function is minimum.
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A chord which passes through the centre is called · A. radius · B. diameter · C. arc · D. none
Answer:
It would be a diameter
Step-by-step explanation:
The diameter is also a chord.
Kiran is flying a kite. He gets tired, so he stakes the kite into the ground. The kite is on a string that is 39 feet long and makes a 40 degree angle with the ground. How high is the kite?
Answer:
100
Step-by-step explanation:
How would you describe Melody's relationship with her mother? (1 point)
• Melody's mother is supportive, but sometimes indifferent.
They have mutual understanding, but not a close bond.
O Melody's mother is supportive at home and school.
O They have a close bond, but not much mutual understanding
Answer: commensalism
Step-by-step explanation:
Melody and her mother aren't hurting each other but also aren't of the same benefit
The relationship that Melody has with her mother is that They have a close bond, but not much mutual understanding.
What is meant by a Story?A story is a fiction or a non fiction narrative which tells us about a series of events or verse, which is narrated in such a way that it takes the interest of the reader.
Most of the fictions convey a certain moral or idea that should be taken in to our life.
Given is a story of a little girl Melody and her mother.
We can clearly seen from the story that, Melody is five year old.
She has a pet named Ollie, which is a fish.
When the fish come out of the bowl by itself, Melody was scared and screamed for help.
But non one heard.
So as a method to rescue Ollie, she put the bowl upside down to save it.
When mother sees it, she misunderstood the situation.
So the relationship between Melody and mother is close bond, but not much mutual understanding.
Hence the correct answer is option D.
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A landowner recently sold a large plot of land. The sale decreased his total acreage. Write two equivalent expressions that represent the new acreage. Use the expressions to describe another way to find the new acreage
The two equivalent expressions for the new acreage sold by the landowner are:
NS = ST - SVNS = ST - (ST - SV)What are the two equivalent expressions that represent the new surface?Both of these expressions will give the same result, which is the new acreage after the sale.
The difference between the total surface area (ST) minus the surface area sold (SV): NS = ST - SV The difference between the total surface area (ST) minus the difference between the total surface area (ST) minus the surface area sold (SV): NS = ST - (ST - SV)Another way to find the new acreage is to subtract the sold acreage from the total acreage. This is the same as the first expression, but it may be easier for some people to understand. For example, if the total acreage was 100 acres and the sold acreage was 20 acres, the new acreage would be 100 - 20 = 80 acres.
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A number decreased by 3 is at least 7
Answer:
Step-by-step explanation:
x-3 is greater than or less than 7
Triangle cde is dilated by a scale factor of 2 to form triangle CDE . Side EC measures 86.
Since triangle CDE is dilated by a scale factor of 2 to form triangle CDE, the measure of side EC is equal to 43 units.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image(original figure)
Substituting the given parameters into the scale factor formula, we have the following;
Scale factor = Dimension of image/Dimension of pre-image
2 = 86/side EC
Side EC = 43 units.
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Complete Question:
Triangle CDE is dilated by a scale factor of 2 to form triangle CDE . Side E'C' measures 86. What is the measure of side EC?
a 6-ounce bottle of medicine contains 36 doses. how many doses are in a 15-ounce bottle of the same medicine?
Answer:
Step-by-step explanation:
If a 6-ounce bottle of medicine contains 36 doses, we can use a proportion to find how many doses are in a 15-ounce bottle:
6 ounces / 36 doses = 15 ounces / x doses
Cross-multiplying, we get:
6 x = 36 * 15
6 x = 540
Dividing both sides by 6, we get:
x = 90
Therefore, a 15-ounce bottle of the same medicine contains 90 doses.
Help me please I am so lost
Answer:
Being lost on this problem is well-earned. I don't know what the question is looking for. There appear to be no options, other than to identify some unique feature of the calculation.
If a polynomial has one root in the form of (a+[tex]\sqrt{b}[/tex]) and a second root in the form of (a-[tex]\sqrt{b}[/tex]) the polynomial must have the form of a^2 + b.
Step-by-step explanation:
I'll take a guess at how this problem wants the sentence to end. We are told there are two roots a polynomial. We can write the polynomial as the product of both roots, which would be equal to zero:
(a+[tex]\sqrt{b}[/tex])*(a-[tex]\sqrt{b}[/tex])
Multiply the factors to obtain:
a^2 - a[tex]\sqrt{b}[/tex] + a[tex]\sqrt{b}[/tex] + ([tex]\sqrt{b}[/tex] )^2
a^2 + b
So one might say:
If a polynomial has one root in the form of (a+[tex]\sqrt{b}[/tex]) and a second root in the form of (a-[tex]\sqrt{b}[/tex]) the polynomial must have the form of a^2 + b.
But that's my guess at something that would be a true statement.
A cell phone plan costs $ 28.90 per month for 400 minutes of talk time. It costs an additional $ 0.05 per minute for each minute over 400 minutes. To get e-mail access, it costs 20% of the price for minutes of talk time. Your bill, which includes e-mail, is the same each month for 7 months. The total cost for all 7 months is $273.91. Write and solve an equation to find the number of minutes of talk time you use each month.
Equation: 273.91 = 7 (0.05m + 28.90 + 0.20(28.90))
Please find the solution.
The number of minutes of talk time used each month is 89. The solution has been obtained by using linear equation.
What is a linear equation?
The linear equation has a degree of 1. It is evident that there are no variables in linear equations with exponents greater than one. This graph's equation produces a straight line.
We are given that a cell phone plan costs $ 28.90 per month for 400 minutes of talk time and the related information.
Let m be the number of minutes of talk time
From this, we get an equation as
273.91 = 7 (0.05m + 28.90 + 0.20(28.90))
On solving the equation, we get
⇒273.91 = 7 (0.05m + 28.90 + 5.78)
⇒273.91 = 0.35m + 202.3 + 40.46
⇒273.91 = 0.35m + 242.76
⇒0.35m = 31.15
⇒m = 89
Hence, the number of minutes of talk time used each month is 89.
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pllssssss hellllppppp
None of the given equations gives the correct answer, the answer is none of the options.
The equation from the calculation is:
y = 375(0.9834)ˣ
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign "=". Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.
The data gives the relation between time and temperature.
We are asked to find the time and temperature relation as an equation.
We are given five equations as options.
a) T(x) = 375(0.5)ˣ
x is time and T is temperature.
Now we will give the value of x = 10 in this equation.
T(10) = 375 * 0.5¹⁰ = 0.366
This is not the value given in the table.
So this is not the equation.
b) T(x) = -50x + 375
T(10) = -50 * 10 + 375 = -500 + 375 = -125
This is not the equation.
c) T(x) = -25x² + 375
T(10) = -25 * 10 * 1 0 + 375 = -2500 +375 = -2125
This is not the equation.
d) T(x) = 50x - 375
T(10) = 50 * 10 - 375 = 500 - 375 = 125
This is not the equation.
e) T(x) = 25x² -75x + 375
T(10) = 25 * 10 * 1 0 -75 * 10 + 375 = 2500 -750 +375 = 2125
The general form of the exponential equation is:
y = abˣ
375 = ab⁰= a
325 = ab¹⁰
275 = ab²⁰
275/325 = b¹⁰
b = 0.9834
So the equation for this data is:
y = 375(0.9834)ˣ
Since none of the given equations gives the correct answer, the answer is none of the options.
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please finish these 4 I need help pls
Find the volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes, the curve y = e^x and the line x = ln 8 about the line x = ln 8. Please show me in two ways (disk/washer method and cylindrical shells method)
the area of the inner cylinder is 2π(e^8/2)ln 8 and the area of the outer cylinder is 2πln 8e^8. The volume is then equal to the integral of the area of the cylindrical
Disk/washer method:
[tex]V = π ∫[ln 8]^8 (e^x)^2 dx\\V = π ∫[ln 8]^8 e^2x dx\\V = π(e^2x/2)|[ln 8]^8\\V = π(e^16 - (e^2(ln 8))^8)/2\\V = (π(e^16 - 64)/2)[/tex]
Cylindrical shells method:
[tex]V = 2π ∫[ln 8]^8 x(e^x) dx\\V = 2π ∫[ln 8]^8 xe^x dx\\V = 2π(x(e^x/2) - (e^x/2)ln x)|[ln 8]^8\\V = 2π((ln 8)(e^8 - 8) - (e^8/2)ln 8)\\V = (2π(e^8 - 64ln 8 - 4e^8))/2\\V = (π(e^16 - 64 - 8e^8))/2[/tex]
The disk/washer method can be used to solve for the volume of the solid generated by revolving the given region about the line x = ln 8. This method involves integrating the area of a ring, which can be formed by subtracting the area of a disk from the area of the washer. In this case, the area of the disk is π(e^2(ln 8))^8 and the area of the washer is π(e^16). The volume is then equal to the integral of the area of the ring, which is π(e^16 - (e^2(ln 8))^8).
The cylindrical shells method can also be used to find the volume of the solid generated by revolving the given region about the line x = ln 8. This method involves integrating the of a cylindrical shell, which can be formed by subtracting the area of the inner cylinder from the area of the outer cylinder. In this case, the area of the inner cylinder is 2π(e^8/2)ln 8 and the area of the outer cylinder is 2πln 8e^8. The volume is then equal to the integral of the area of the cylindrical
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how to write a quadratic function in standard form y = 4 (x-1)^2 + 5
Toby goes on holiday to Geneva, Switzerland. In Geneva, Toby sees a watch costing 193. 75 CHF (Swiss Francs). In Manchester, an identical watch costs £145. Given that £1 = 1. 55 CHF
a) In which city is the watch cheaper?
b) By how much is it cheaper (in £)?
To answer this question, we will need to convert the price of the watch in Geneva to pounds and compare it to the price of the watch in Manchester.
First, let's convert the price of the watch in Geneva from CHF to pounds:
193.75 CHF ÷ 1.55 CHF/£ = 125 pounds
Now, we can compare the price of the watch in Geneva to the price of the watch in Manchester:
125 pounds (Geneva) < 145 pounds (Manchester)
Therefore, the watch is cheaper in Geneva.
To find out by how much it is cheaper, we can subtract the price of the watch in Geneva from the price of the watch in Manchester:
145 pounds - 125 pounds = 20 pounds
So, the watch is 20 pounds cheaper in Geneva.
In conclusion, the watch is cheaper in Geneva by 20 pounds.
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Please help ASAP! Thanks
Find the equation
to the line below.
Y= __ __ /__ x
[tex]{ \qquad \qquad \huge \rm \underline{ \underline{ \Répondre}}} [/tex]
lets find the equation of line in two point form, considering points (0 , 0) and (-3 , 4)
[tex]\qquad \rm\dashrightarrow \:y - 0= \dfrac{4 - 0}{ - 3 - 0} (x -0)[/tex]
[tex]\qquad \rm\dashrightarrow \:y = - \dfrac{4 }{ 3 } x [/tex]
That's the required equation ~
You can also simply it as :
[tex]\qquad \rm\dashrightarrow \:3y= - 4x[/tex]
[tex]\qquad \rm\dashrightarrow \:4x + 3y = 0[/tex]
how many teaspoons is 10 ml
Using the formula, we can convert milliliters to teaspoons. 1 milliliter equals 0.202 teaspoons, thus 10ml equals 2.02 teaspoons.
The volume unit is milliliters. A teaspoon is also a volume measure, however it is a smaller unit that is commonly used at dinner settings.
One millilitre is equivalent to 0.202 US teaspoons using normal conversion rates.
As a result, we may define the link using the unit conversion idea.
One milliliter is equal to 0.202 teaspoons in the United States.
For example, 10 milliliters equals 2.02 teaspoons.
As a result, we'll need roughly 2 tablespoons to get 10 ml.
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prove that if a symmetric matrix is invertible, then its inverse is symmetric also.
Let A be a symmetric matrix that is invertible. This means that there exists a matrix B such that AB = BA = I, where I is the identity matrix. We want to show that B is also symmetric, that is, [tex]B = B^{T}[/tex]
To prove this, we can use the definition of matrix inversion. We know that AB = I, so we can take the transpose of both sides:
[tex]AB^{T} = I^{T}[/tex]
Using the transpose rules, we can rewrite this as:
[tex]B^{T} * A^{T}[/tex] = I
Now, we can multiply both sides of this equation by A:
[tex]B^{T} * A^{T}[/tex]* A = A
Since A is invertible, we can multiply both sides by A⁻¹ to get:
[tex]B^{T}[/tex] = A⁻¹
Therefore, we have shown that the inverse of a symmetric matrix A, which we denote as A⁻¹, is also symmetric, since A⁻¹ = [tex]B^{T}[/tex], which is the transpose of the matrix B.
Hence, we have proved that if a symmetric matrix is invertible, then its inverse is symmetric as well.
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A new car is purchased for 21,100 dollars. The value of the car depreciates at a rate of 2% per year. Which equation represents the value of the car after 5 years?
the equation that represents the value of the car after 5 years is Value of car after 5 years = 21,100 x 0.98^5 = 19,105.08
How to calculate the equation that represents the value of the car after 5 yearsGiven:
The cost price of the car, P = $21100,
The depreciation rate = 2%
Calculate the value of the car after 6 years by the following formula,
A = P (1- r / 100)ⁿ
Here A is the value of the car after 6 years.
Substitute the values,
A = 21100 × (1- 2 / 100)^5,
A = $19,105.08
Therefore, the equation that represents the value of the car after 5 years is Value of car after 5 years = 21,100 x 0.98^5 = 19,105.08
How much would $10,000 due in 50 years be worth today if the discount rate were 7.5%? a $285.02 b. $266.20 c. S204.36 d. $217.80 e $268.89
The amount would $10,000 due in 50 years be worth today if the discount rate were 7.5% is,
P = $7,042
What is mean by Percentage?
A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
We know that;
The formula is,
⇒ Amount = P (1 + r)ⁿ
Hence, We get;
10,000 = P (1 + 0.75)⁵⁰
10,000 = P (1.75)⁵⁰
10,000 = P × 1.42
P = 10,000 / 1.42
P = $7,042
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